Journal of Formalized Mathematics
Volume 4, 1992
University of Bialystok
Copyright (c) 1992
Association of Mizar Users
Properties of Caratheodor's Measure

Jozef Bialas

University of Lodz
Summary.

The paper contains definitions and basic properties of
Ca\ra\the\o\dor's
measure, with values in $\overline{\Bbb R}$, the enlarged set of real
numbers, where $\overline{\Bbb R}$ denotes set $\overline{\Bbb R} =
{\Bbb R}\cup\{\infty,+\infty\}$  by [10].
The article includes the text being a continuation of the paper
[5]. Caratheodor's theorem and some
theorems concerning basic properties of Caratheodor's measure are proved.
The work is the sixth part of the series of articles concerning the Lebesgue
measure theory.
The terminology and notation used in this paper have been
introduced in the following articles
[11]
[8]
[13]
[12]
[14]
[6]
[7]
[1]
[9]
[2]
[3]
[4]
[5]
Contents (PDF format)
Bibliography
 [1]
Grzegorz Bancerek.
The fundamental properties of natural numbers.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Jozef Bialas.
Infimum and supremum of the set of real numbers. Measure theory.
Journal of Formalized Mathematics,
2, 1990.
 [3]
Jozef Bialas.
Series of positive real numbers. Measure theory.
Journal of Formalized Mathematics,
2, 1990.
 [4]
Jozef Bialas.
The $\sigma$additive measure theory.
Journal of Formalized Mathematics,
2, 1990.
 [5]
Jozef Bialas.
Completeness of the $\sigma$additive measure. Measure theory.
Journal of Formalized Mathematics,
4, 1992.
 [6]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [9]
Beata Padlewska.
Families of sets.
Journal of Formalized Mathematics,
1, 1989.
 [10]
R. Sikorski.
\em Rachunek rozniczkowy i calkowy  funkcje wielu
zmiennych.
Biblioteka Matematyczna. PWN  Warszawa, 1968.
 [11]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [12]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [13]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
Received June 25, 1992
[
Download a postscript version,
MML identifier index,
Mizar home page]